On Kemnitz' conjecture concerning lattice-points in the plane

Abstract

In 1961, Erdos, Ginzburg and Ziv proved a remarkable theorem stating that each set of 2n-1 integers contains a subset of size n, the sum of whose elements is divisible by n. We will prove a similar result for pairs of integers, i.e. planar lattice-points, usually referred to as Kemnitz' conjecture. © 2006 Springer Science + Business Media, LLC.